Curvature Properties of Generalized pp-Wave Metrics.
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Authors: A. ALI SHAIKH, T. Q. BINH AND H. KUNDU
DOI: 10.46793/KgJMat2102.237S
Abstract:
The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P ⋅ P = −
Q(S,P).
Again we investigate the sufficient condition for which a generalized
pp-wave spacetime turns into pp-wave spacetime, pure radiation
spacetime, locally symmetric and recurrent. Finally, it is shown that the
energy-momentum tensor of pp-wave spacetime is parallel if and only if it is
cyclic parallel. Again the energy momentum tensor is Codazzi type
if it is cyclic parallel but the converse is not true as shown by an
example. Finally, we make a comparison between the curvature
properties of the Robinson-Trautman metric and generalized pp-wave
metric.
Keywords:
Einstein field equations, Brinkmann-wave metric, pp-wave metric, generalized pp-wave metric, Robinson-Trautman metric, Einstein manifold, quasi-Einstein manifold, 2-quasi-Einstein manifold, generalized quasi-Einstein manifold in the sense of Chaki, recurrent type curvature condition, pseudosymmetry type curvature condition.
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